Expansion of electric power grids with renewable energies will see an increased utilization of power converters for generation, transmission and energy storage. In order to keep the power system operable and highly reliable steady state voltage and transmission angle stability have to be ensured besides transient stability. These fundamental requirements are of particular concern in AC grids with weak converter connection points.
Weak AC grids are prone to voltage instability and subsequent voltage collapse if there is a reactive power unbalance. Voltage instability designates a power system state where the profile of node voltages cannot be kept above a certain desired voltage level. If further decline of AC voltage cannot be stopped voltage collapse is impending. Voltage collapse can occur, e.g., in connection with reactive power supply by capacitors, stalling asynchronous motors, over-excitation limitation of synchronous generators or if consumer load voltages are controlled via on-load transformer tap changers. The voltage collapse process is a dynamic process involving inherent or external closed-loop control characteristics.
Being relevant for the present invention voltage collapse is also known from current sourced line-commutated converters of High Voltage Direct Current (HVDC) transmission systems (FIG. 1-a) operating on weak AC grids. A didactic explanation of voltage stability associated phenomena at HVDC terminals is presented by Pilotto, Szechtman and Hammad in their paper on “Transient AC Voltage Related Phenomena for HVDC Schemes Connected to Weak AC Systems”, appearing in IEEE Trans. on Power Delivery, Vol. 7, No. 3, pp. 1396-1404, 1992. This paper describes on page 1398 the importance of the voltage sensitivity factor to determine potential regions of voltage instability at an ac/dc junction. The “voltage sensitivity factor” method was first practically applied for the design of the Blackwater Back-to-Back Tie in Clovis, N. Mex., USA. See the paper by Kühn, Hammad, Güth, Neidhart: “Design and Control Strategies of HVDC Schemes for AC Voltage Control and Stabilization” presented at the Int. Conf. on DC Power Transmission in Montreal, June 1984, pp. 105-108 of the conference proceedings. Hammad's and Kuhn's paper “A Computation Algorithm for Assessing Voltage Stability at AC/DC Interconnections”, IEEE Transactions on Power Systems, Vol. PWRS-1, No. 1, February 1986, provides an in-depth treatment.
Lee and Andersson summarize existing analytical methods and include own work on that subject—particularly on multi-infeed arrangements—in their paper “Voltage and Power Stability of HVDC Systems—Emerging Issues and New Analytical Methodologies”, VII SEPOPE, Curitiba, Brazil, 23-28 May 2000. Practically relevant for controller design remain the a.m. “voltage sensitivity factor” and the related “voltage-power characteristic” both identifying the maximum transferrable power of the network for given network conditions. This information on critical network conditions is used during operation with the intention to circumvent unstable operating regions. This, however, cannot be guaranteed for the future where grid expansion changes the unstable operating regions.
A safe way to prevent voltage instability is the utilization of a static compensator as, e.g., the STATCOM. IEEE Special Publication “Voltage Sourced Converter (VSC) Applications in Power Transmission”, no. 08TP200, refers to this device in sec. 3.1 as a “specific application for the compensation of DC transmission”. The use of a STATCOM is only justifiable in weak AC grids. A DC link operating on a normally strong AC grid does not need and does not use a STATCOM. Then reduction of the short circuit power capacity through an unexpected fault or unplanned switching event may cause unstable conditions and voltage collapse if no countermeasures are taken. For line-commutated converters there exist presently two different countermeasures, one of which is described by Bunch and Kosterev in their paper “Design and Implementation of AC Voltage Dependent Current Order Limiter at Pacific HVDC Intertie”, IEEE Transactions on Power Delivery, PE-408-PWRD-0-01-1999. Voltage Dependent Current Order Limitation (VDCOL) was introduced into the PDCI (Pacific HVDC Intertie) controls to cope with new operating conditions due to environmental requirements (see chapter III of the paper). Main reason for the implementation of VDCOL was the Aug. 10, 1996 WSCC outage in the USA.
The second measure reduces spontaneously the power order at the occurrence of certain network conditions as described in the a.m. paper “Design and Control Strategies of HVDC Schemes for AC Voltage Control and Stabilization” on page 106, text below FIG. 1. Here for a Back-to-Back Tie the nominal power of 200 MW is reduced to 60 MW to cope with the reduced SCR-value at an AC line trip following a three phase short circuit. VDCOL is not always reliable since for very weak converter connection points the depression of AC voltage at the stability limit is not high enough to actuate VDCOL. The converter can then suddenly and without any early indication go from stable to unstable as depicted in FIG. 5-a of the inventor's paper “Control and Stability of Power Inverters Feeding Renewable Power to Weak AC Grids with No or Low Mechanical Inertia”, IEEE Power Systems Conference and Exhibition, Seattle, USA, 15-18 Mar. 2009. The second measure—which can be called Event Actuated Power Order Reduction (EAPOR)—requires exact knowledge of the maximum transferable power levels for all possible system operating states including worst case contingencies. With ongoing installations of renewable generation facilities and corresponding changes of the load flow it will be difficult if not impossible to keep track of necessary modifications of the power reduction schedule.
After all it can be stated: presently implemented real-time controls do not reliably prevent voltage collapse when operating on a weak AC grid.
Besides the above treated classical line-commutated converters now self-commutated voltage sourced converters play an increasingly important role in HVDC power transmission. Contrary to classic HVDC transmission these converters permit continuous voltage control in addition to real power transfer. Power from off-shore wind farms will predominantly be transmitted via HVDC links using voltage sourced self-commutated converters. These converters are also preferably used for distributed generation of renewable energies (solar cell facilities, fuel cells, battery storage plants and frequency converters) on medium and low voltage level.
Since the voltage-sourced self-commutated converter will be equipped with defined voltage control capability voltage stability is usually not considered as a problem. Even when the internal converter voltage hits its ceiling the voltage is at least supported. Frequency stability as it is often addressed in connection with the substitution of rotating synchronous generators by self-commutated converters can actually be achieved through implementation of artificial rotating mass in converter controls as shown in the before mentioned paper.
Another type of instability relates to the transmission angle of the network the converter is connected to. For a radial system the transmission angle is the difference of the phase angles of the terminal voltages of a radial AC line. For a meshed network it refers to the difference between Thevenin's equivalent voltage and the terminal voltage. From the voltage magnitude no conclusion can be drawn regarding the transmission angle. The voltage control capability of the converter can even hide transmission angle instability. This can be considered as a major problem in future power grids if not adequately addressed and cured. Transmission angle instability can lead to loss of synchronism. The currently envisaged use of Voltage Phasor Measurements via the Global Positioning System (GPS) cannot be considered as remedial measure in connection with converters since a state estimator including converters, converter based transmission systems and controls, particularly control limits, is not available at the time being. The following describes the mechanism leading to transmission angle instability.
In general it is assumed that voltage sourced self-commutated converters can easily cope with weak system conditions. Actually they do not need at all an active AC grid and they can provide continuous voltage control. However, a digital computer study conducted for the present invention showed that also self-commutated converters can cause instability in connection with weak AC grids. The study holds for a simple generic but nevertheless representative equivalent circuit (FIG. 1-b). Diagrams showing the dependency between real power (P) and reactive power (Q) (FIGS. 1-c and 1-d) as well as time line diagrams of converter and AC grid quantities reveal possible stability problems: FIG. 3-a, 3-b, 4-a, 4-b and 4-c hold for unlimited reactive power supply capability and FIG. 5-a, 5-b, 6-a, 6-b and 6-c for limited reactive power supply capability of the self-commutated converter.
The PQ-diagrams (FIGS. 1-c and 1-d) given here hold for equal magnitudes of the internal (V0) and terminal (V1) AC voltages (FIG. 1-b). For different voltages (V0, V1) the diagram shifts along the Q-axis and the circle diameter changes in proportion to the product of the voltages. The circle will be transposed horizontally when there is a parallel capacitance at the AC converter terminal (either, e.g., stemming from a compensating condenser or from an AC line). This shift on the Q-axis has to be considered for the stability analysis described further below.
Operating point “a” in FIGS. 1-c and 1-d holds for a closed switch (S) (FIG. 1-b). Operating point “b” holds for an open switch (S). The power angle of the inverter (δinv,a, δinv,b) and the power transmission angle (δ1a, δ1b) of the AC grid adopt values in accordance with the power transfer level and the values of the coupling reactance Xinv (Xinv,a, Xinv,b) and the grid reactance (Xa, Xb). Since for the present simulations the phase angle of the equivalent internal AC voltage is chosen as zero, the power transmission angle δ1 has the same value as the phase angle phase_V1 of the AC terminal voltage.
When the switch (S) is opened the power (P) reduces immediately down to the value at operating point “b” which is lower than the maximum transferable power (MTP) of the AC-grid. The MTP-level can be calculated fromP=(V1×V0×sin δ1b)/Xb 
The converter power controller detects the power control error and responds by increasing the phase angle (phase_Vq1) of the internal converter voltage (Vq1) to compensate for this error. However, the real power supplied by the inverter can not become larger than the MTP-level. Because the controller does not know the value of the MTP-level it will increase the DC current beyond the MTP-point and actually decrease the real power. If not stopped through protective measures the operating point will cycle through inverter and rectifier operation (FIG. 1-d).
FIGS. 3-a and 5-a show this cycling via the depiction of power/angle-trajectories. FIG. 3-a holds for inverter controlled AC voltage without reactive power supply limitation. FIG. 5-a holds for limited reactive power supply capability. FIGS. 3-b and 5-b show the corresponding phase angles of the AC terminal voltage (phase_V1) and the converter internal voltage (phase_Vq1). Their difference is the converter's power angle.
The changing radius of the converter PQ-Diagram (FIG. 1-d) reflects the change of the reactive power supply requirement when the operating point moves from “a” to “b” and then through the bold solid circle clockwise from “b” via “c” to “d” and then back to “b”. For the situation depicted in FIG. 1-d the rated converter power (line-dotted circle going through “a” and “d”) is not exceeded. That is, the inverter controls the AC voltage magnitude (V1) (FIG. 4-c) also within the unstable region of the transmission angle (phase_V1) (FIG. 3-a). If the unstable operating point “d” of the grid PQ-diagram (FIG. 1-d) would lie outside rated converter power the AC voltage would decrease, however, it does not collapse (FIG. 6-c). The AC voltage magnitude is, therefore, no proper criterion to predict an impending instability.
After opening the switch (S) (FIG. 1-b) transmission angle instability occurs in both the cases, for fully controllable AC terminal voltage as well as for limited control. For full voltage control the stability limit lies at 90° (FIG. 3-a), limited voltage control yields an angle of 75° (FIG. 5-a).
Wide-system outages in all parts of the world occurring during the last decades have enforced research work in the power system community to understand better the voltage collapse phenomena and to find methods and tools to solve the problem. Considering the immense consequences of outages for economy and daily life these investigations are necessary and urgent, particularly in light of the planned power generation additions using large amounts of wind power and in contrast to this, the inadequacy of the actual power grids. Loss of revenues can sum up to millions of dollars for such systems as the WSCC grid if outages last several hours.
Fundamental contributions are Cutsem's paper on “Voltage Instability: Phenomena, Countermeasures, and Analysis Methods”, Proceedings of the IEEE, Vol. 88, No. 2, February 2000, p. 208-227, and the IEEE Special Publication “Voltage Stability Assessment: Concepts, Practices and Tools”, Product No. SP101PSS, August 2002. Both the publications deal with pure AC systems, except for a short hint on page 215 of Cutsem's paper on HVDC modulation—last section before chapter IV. Specifics of converter related problems are not covered although HVDC transmission systems have a very strong impact on grid stability as shown by Hammad in his paper on “Stability and Control of HVDC and AC Transmission in Parallel”, IEEE Trans. on Power Delivery, Vol. 14, No. 4, pp. 1545-1554, October 1999. The coupling of the transmission angle of a parallel AC/DC transmission with the AC terminal voltage of the converters introduces even more complexity into the problem then a pure DC transmission does. Also here application of the voltage sensitivity factor is possible as mentioned on page 1550 of the paper.
Patents and patent application publications reviewed by the author relate to voltage stabilization in AC power systems with no particular features for interconnected AC/DC systems. The subsequent assessment of their meaning for converter equipped power systems shows that these patents as to the judgment of the author are not usable for an avoidance of voltage collapse in AC/DC systems.
European Patent EP 1 723 482 B1, Pub. Date: Apr. 9, 2008, relates to a special method for voltage stabilization when using a transformer. The proposed controls are meant to operate in case of dynamic instabilities. I.e., after a line and/or load impedance change the power grid is still statically capable of meeting the real power request. This does not cover static unbalance of power demand and transferable power which is the reason for steady state voltage instability and following dynamic voltage collapse.
U.S. Pat. No. 6,219,591 B1, Date of Patent: Apr. 17, 2001, and U.S. Pat. No. 6,249,719 B1, Date of Patent: Jun. 19, 2001, relate to a voltage instability predictor identifying in real time proximity to the stability limit and providing a signal which can be used, e.g., to impose a limit on loading or to shed load when the limit is exceeded, to block on-load tap changing (OLTC) transformers or to enhance static VAR systems which can mask an imminent voltage collapse. A certain margin between actual power and maximum transferable power should not be exceeded to reliably avoid instability. However, selection of the margin involves heuristics, i.e., the estimation of closeness to instability is not secure. Also it is doubtful whether the method can be applied for converters at all because of control limits becoming effective at certain operational conditions leaving no time for the necessary estimation process. And if it could be applied it would only provide load-shedding by reducing the power set value of the converter. This would not be a stabilization method with automatic adaption to maximum transferable power as it is desired for maximum efficiency.
United States Patent Application Publication US 2003/0011348 A1, Pub. Date: Jan. 16, 2003, discusses possible combinations of conventional and renewable generation facilities, including converters and a so called co-active controller. However, specific converter related methods and apparatus for automatic voltage and transmission angle stabilization are in no aspect addressed and clarified, particular the problem of voltage collapse, the underlying destabilizing phenomena and related concrete mitigating converter implemented methods and means are no subject in that material.
According to the current state of the art there is no secure method available detecting instability of the line-commutated or self-commutated converter and conducting an operation with maximum transferrable network power.